YYou can send a text to someone by using phone number @vzwpix.com. (email@example.com). This you can send pictures as well. Use @vtext.com for a simple sms text. You cannot see your texts on your computer only on your phone.
OR use the PC app;
1- Make sure you are using Verizon Message on your mobile
2. Please check if you are subscribed to INTEGRATED MESSAGING on the Mobile. In order to do that – Launch Verizon Messages - go to Settings – under integrated Messaging feature make sure that you are Subscribed.
If you ARE Subscribed , you will see the Unsubscribe option. If you are not subscribed, select ‘subscribe’.
3. If you did not install the PC app recently from this page, please uninstall it. Then, install the PC app from the 'Download Desktop App' button on the Verizon Wireless website.
NOt not sure if you can read texts sent from your phone on this app, I've never used it.
also, firstname.lastname@example.org and text.com are good only to Verizon customers. I'm sure other providers have their own addresses as well.